Stability and Convergence Analysis of Unconditionally Energy Stable and Second Order Method for Cahn-Hilliard Equation
Received:October 27, 2022  Revised:August 12, 2023
Key Words: error analysis   unconditional energy stability   IEQ   Cahn-Hilliard equation  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.12261017; 62062018), the Science and Technology Program of Guizhou Province (Nos.ZK[2022]006; ZK[2022]031; QKHZC[2023]372), Shanxi Province Natural Science Research (Grant No.202203021212249), the Scientific Research Foundation of Guizhou University of Finance and Economics (Grant No.2022KYYB08), the Innovation Exploration and Academic Emerging Project of Guizhou University of Finance and Economics (Grant No.2022XSXMB11) and the Special/Youth Foundation of Taiyuan University of Technology (Grant No.2022QN101).
Author NameAffiliation
Yu ZHANG School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China 
Chenhui ZHANG College of Mathematics, Taiyuan University of Technology, Shanxi 030024, P. R. China 
Tingfu YAO College of Science, Guiyang University, Guizhou 550005, P. R. China 
Jun ZHANG Computational Mathematics Research Center, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China 
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      In this work, we construct an efficient invariant energy quadratization (IEQ) method of unconditional energy stability to solve the Cahn-Hilliard equation. The constructed numerical scheme is linear, second-order accuracy in time and unconditional energy stability. We carefully analyze the unique solvability, stability and error estimate of the numerical scheme. The results show that the constructed scheme satisfies unique solvability, unconditional energy stability and the second-order convergence in time direction. Through a large number of 2D and 3D numerical experiments, we further verify the convergence order, unconditional energy stability and effectiveness of the scheme.
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